FEYZA ESRA ERDOĞAN, Cumali YILDIRIM

On a Study of the Totally Umbilical Semi-Invariant Submanifolds of Golden Riemannian Manifolds

The Golden Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Golden Structure will be called a Golden Riemannian manifold. Precisely, we can say that an (1,1)-tensor field on a m-dimensional Riemann manifold is a Golden structure if it satisfies the equation , where is identity map on . Furthermore, , the Riemannian metric is called -compatible and is named a Golden Riemannian manifold. The main purpose of the present paper is to study the geometry of Riemannian manifolds endowed with Golden structures. For this purpose, we study totally umbilical semi-invariant submanifold of the Golden Riemannian manifolds. Also, we obtain integrability conditions of the distributions and investigate the geometry of foliations.

Anahtar Kelimeler:

Semi-invariant submanifolds, Golden Riemannian manifolds, totally umbilical submanifolds

On a Study of the Totally Umbilical Semi-Invariant Submanifolds of Golden Riemannian Manifolds

Keywords:

Semi-invariant submanifolds, Golden Riemannian manifolds, totally umbilical submanifolds,

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